GO ON THE CONDUCTIVITY, SPECIFIC GRAVITY AND 



It might be well to note that in each series having a constant 

 concentration of potassium sulphate, the differences seem to 

 change from a negative to a positive per cent. 1 



Considering the many sources of error in the calculations of 

 the conductivity, the agreement between the observed and 

 calculated values is very satisfactory, and leads one to draw the 

 conclusion that the conductivity of mixtures of solutions of these 



1 Note by the communicator of the paper. Mr. Barnes points out that in series of 

 mixtures whose constituent solutions have in the case of one electrolyte the same con- 

 centration (n i say) in all. and in that of the other a variable concentration (n% say), the 

 excess (e) of the calculated over the observed value of the conductivity increases with 

 n-2, being usually negative for small values of n% and positive for larger values. At 

 first sight it might appear that he had over-estimated his limit of error, and that the 

 conductivity was thus shown to be calculable only for a particular value of n% in each 

 case. There are, however, two sources of error which will account for this regular 

 progression in the relative magnitude and sign of the e's, viz.. (1) The employment, 

 of the quotients of the specific equivalent conductivity by the specific equivalent con- 

 ductivity at infinite dilution (///,) as the values of the ionization coefficients (a) 

 for simple solutions, and (2) the impossibility of drawing with perfect accuracy the 

 dilution-ionic-concentration curves. The more concentrated the solutions the greater 

 will/>/ao differ from ; and the greater tho liability to error in the drawing of the 

 curves the greater the possible error in the determination of the ionization coefficients 

 of the electrolytes in the mixture. The dilution-ionic-concentration curves are nearly 

 rectilinear for very weak and for strong solutions but curve rapidly in the region of 

 moderate dilution, and it is in this region that it is most difficult to draw them 

 accurately. Hence in the case of strong solutions, the magnitude and sign of the e's will 

 be determined largely by the error due to using values of fi//iiao as the ionization coeffi- 

 cient* of the simple soi ut ions. In the case of moderately dilute solutions they will be 

 determined by both sources of error. In the case of dilute solutions neither source of 

 error will have so large an effect on the result. Hence a regular progression of the e's 

 the same in kind, may be expected in different series of mixtures of strong solutions of 

 two given electrolytes ; a regular progression may be expected also in series of moder- 

 ate dilution, but since the error due to inaccurate drawing of curves will depend on the 

 portion of the curve which is used, it may be different in kind for different series ; and 

 in sufficiently dilute solutions no regular progression is likely to occur. The most of 

 Mr Barnes' series are of moderate dilution, and in all of them the e's show a regular 

 progression of the same kind, as they would if the errors involved did not conflict in 

 sign, or if the error due to the one source were large relatively to that due to the other. 

 His series of dilute solutions exhibit the same progression in the e's, but they consist of 

 only two mixtures each. In my calculations of the conductivity of mixtures of 

 NaCl and KC1 solutions (Trans N. S. I. S., 9, 116), the three more concentrated series 

 showed a progression of the e's of the same kind, the two weakest series showed no 

 progression. In Mr. Macintosh's calculations (Ibid., 9, 132), for HC1 and XaCl, 

 the two stronger series gave a progression of the same kind, the weakest no progression. 

 And in Mr. Archibald's calculations (/6W.,9, 299), for K 2 So 4 and NaaS0 4 solutions, the 

 four stronger series gave progressions of the e's, differing in kind, and the three series 

 of weaker solutions gave either a very doubtful progression or no progression at all. 

 All these results are thus consistent with the assumption that this regular progression in 

 the e's is due ma nly at least to the two sources of error mentioned above. J. G. M. 



